A FRESH PERSPECTIVE ON U.S. MUTUAL FUNDS’ PERFORMANCE

ATTRIBUTION, FACTOR MODEL AND QMJ

by

Xin Zhu

Bachelor of Business Administration, Camosun College 2011

Bachelor of Engineering, Beijing University of Technology 2004

and

Xiao Guang, Zhang

Bachelor of Economics, University of Queensland 2007

PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN FINANCE

In the Master of Science in Finance Program

of the

Faculty

of

Business Administration

© Xin Zhu, Xiaoguang Zhang 2015

SIMON FRASER UNIVERSITY

Term (Summer) Year 2015

All rights reserved. However, in accordance with the Copyright Act of Canada, this work

may be reproduced, without authorization, under the conditions for Fair Dealing.

Therefore, limited reproduction of this work for the purposes of private study, research,

criticism, review and news reporting is likely to be in accordance with the law,

particularly if cited appropriately.

ii

Approval

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iii

Abstract

In this paper we evaluate the performance of the US mutual fund industry over the

past 15 years, using a novel methodology developed by AQR Management’s Quality

Minus Junk paper (2013). We augment the standard regression models of Fama-French

used in the literatures with a new factor, the Quality Minus Junk factor, which is a

quality-ranking factor developed by the AQR Management. (Quality Minus Junk) 2013

Previously, conflicting evidence was recorded with regard to the merits of the mutual

fund industry, and we believe this could be a result of the preceding researches were

constructed based on the Fama–French three-factor model (FFM) and its various

variations. Despite the FFM’s prominent position in the asset-pricing field, it is subject to

one critical limitation when it comes to evaluating active returns; no meaningful factor to

directly quantify and evaluate the effects of active returns, as all existing factors are

systematic in nature while active returns are idiosyncratic in nature largely. By

incorporating the QMJ factor in the FFM framework, we hope to help investors better

understanding their actively managed portfolios, as this unique factor is constructed

based on four profoundly used fundamental metrics by the investment industry. We are

still unable to use this factor to underpin the mutual industry as our results exhibit

inconsistencies in the QMJ loadings despite QMJ’s strong statistic and theatrical

supports. Adding the Market-Factor results in the QMJ factor insignificant 70% of the

time, adding more of the standard-factors we see that only 50% of the time the QMJ

loadings are significant, around 40% of the time the QMJ loadings are in the negative

zone. Therefore, we believe this shows inconsistence in QMJ’s factor loadings.

Furthermore, we identified consistent alphas (intercepts) in our regressions and we

believe that combining Fama-French and QMJ factor still cannot explain all returns

variations.

iv

v

Executive Summary

This thesis provides an analysis and evaluation of the US mutual fund

performance, and the investment styles they typically use.

Previous mutual performance studies suggest that there is mixed evidence to

support mutual industry as some studies claimed that excessive returns above

benchmarks is function of luck, while others found evidence that the very top performers

tend to remain in their rankings. A through study of the leading factor models in the field

of Asset Pricing Theory indicates that these models concentrate on systematic factors, but

active returns should to be a function of non-systematic factors; specific investment

managers’ skills and experience to select quality companies. Therefore, we should

include an additional quality factor to the existing models if we want directly evaluating

active returns.

We follow the methodology of AQR Management who developed a new factor

called Quality Minus Junk factor (QMJ). This paper demonstrates that using this special

factor they were able to generate retrospect high excessive risk adjusted return, which is

not directly explained by the systematic factors found in FFM and its existing variations.

We apply this factor in the context of mutual fund performance evaluation analysis. We

combine QMJ factor with the standard three and four factor Fama and French models.

Our analysis employs monthly data, and our specifications are adjusted for fixed effect to

control for firm and portfolio specific effects in our estimation. Risk premiums are

calculated by subtracting risk free rates away, and risk free rates are historical monthly

data on 90-day T-bill yield US Treasury bill rates.

We performed six separated sets of regressions with fund returns as dependent

variables; 1) fund returns with QMJ, 2) fund returns with QMJ and Market, 3) fund

vi

returns with SMB, HML, and Market, 4) fund returns with SMB, HML, Market and

QMJ, 5) fund returns with SMB, HML, Market and the UMD (Momentum factor), 6)

fund returns with SMB, HML, Market, UMD, and QMJ.

The regression results are presented in the appendices from Table 1 to 6, and

Graph 1, 2, 3, and 4. The estimation results show that there is no meaningful

improvement in regression R-squares by adding the QMJ factor to the standard factor

model and there is not consistence in QMJ factor loadings as some showing positive

while others showing negative values. Moreover, 50% of all the QMJ loadings appear to

be insignificant at 5% significance level except in first set of regressions where QMJ is

the only independent variable. Therefore, we conclude that is no clear evidence to

support the hypothesis that mutual funds as active investors tend to focus on quality

companies. One interesting finding suggests that the QMJ factor and Market factor and

other systematic factors tend to behave differently.

However, there is also strong evidence to support alphas across all regression as

the intercepts of all regressions are almost significant except a few, and they are ranging

from -0.05 to 0.06, following the same orders of the worst performing funds to the best

performing funds. This could suggest that US mutual fund managers apply techniques

other than quality selection or their metrics for quality selection are different from our

QMJ factor. These alphas represent their uniqueness, as they cannot be explained by the

factors we include in our regressions.

Some of the limitations: the finding only pertaining to US mutual fund industry,

only 15 years of data were included in the analysis but the US mutual industry has been

around more than a few decades, combining FFM with QMJ might not be the best

description of reality. As our data including 2008 -2009 crisis, during the crisis all

investments were sold regardless their quality due to liquidity constrains, this period data

could have screwed our analysis. We think future study could exclude this extreme

period. Furthermore, we suggest that more research needed to conduct to refining the

QMJ factor, to test against more countries’ mutual fund industries, to avoid sampling

vii

problem by only including the truly active funds, and perhaps further exploring the

empirical and theoretical reasons behind the negative relationship between QMJ and

other systematic factors.

viii

Acknowledgements

We would like to thank our thesis supervisor Dr. Christina Atanasova for her

academic and professional advice in helping us bring this interesting work to a higher

academic level. In addition, we also would like to thank our secondary supervisor Dr.

Evan Gatev for his time spent with us in constructing this thesis. Our special thanks go to

all the professors in the Simon Fraser University Beedie School of Business whose

inspirations have been of great support to us.

Our thanks extend to our family members for their continuous support, love and

encouragement; this interest idea could not be developed into a complete thesis and

accomplished without them. We would like extending our appreciation to AQR

Management for their original QMJ idea and analysis, as we were greatly intrigued by

their original and extraordinary ideals. Furthermore, we would like to thank our

employers, for their immense understanding of our situation; whenever we need time off

they were willing to accommodate.

.

ix

Table of Contents

Approval .......................................................................................................................................... ii Abstract .......................................................................................................................................... iii Executive Summary ......................................................................................................................... v Acknowledgements ...................................................................................................................... viii Table of Contents ............................................................................................................................ ix

1: Introduction ................................................................................................................................ 1

2: Previous Literature .................................................................................................................... 7

2.1 Asset Pricing ........................................................................................................................... 7 2.2 Mutual Funds’ Performance .................................................................................................. 11

3: Data and Methodology ............................................................................................................. 14

3.1 Factors’ data and Methodology ............................................................................................. 14 3.1.1 Fama and French Four Factors .................................................................................. 14 3.1.2 QMJ factors ............................................................................................................... 15

3.2 Mutual Funds’ Data and Methodology ................................................................................. 17 3.2.1 Cleaning data ............................................................................................................ 18 3.2.2 One year lagged return .............................................................................................. 18 3.2.3 Assign funds to 10 portfolios .................................................................................... 19

3.3 Main Statistical Test .............................................................................................................. 19

4: Results ....................................................................................................................................... 21

5: Implications and Conclusions ................................................................................................. 26

6: Appendix ................................................................................................................................... 29

7: Reference: ................................................................................................................................. 40

7.1 Mutual Funds’ Researches .................................................................................................... 40 7.2 Asset Pricing Researches ...................................................................................................... 41

________________________________________________ ........................................................ 43

1

1: Introduction

The primary focus of this research is to modify the existing FFM with an intuitive

quality factor that can help us better understanding the active mutual fund industry.

Previous studies have provided us with a lot of evidences to repudiate the active mutual

fund industry, as their performance appeared to be inconsistent and lacklustre. Evidence

shows that there is no much performance persistent, i.e. this period’s winner are not more

likely to be the next period winners, and also some previous studies demonstrate that

excessive returns above benchmarks is a just a function of luck. However, the fact that

most of the previous studies were constructed by employing the FFM or its variations

concerns us in two ways; first, the FFM congenitally lacks strong theoretical support

despite high degree of goodness of fit, second, existing FFM variations also cannot

directly measure active manager’s skills. Most active managers claim that they apply the

concept of “quality at a reasonable price” approach throughout their investment process

as they intend to invest in quality companies in pursuit of active returns. Therefore, we

believe that FFM’s second shortcoming is particularly acute amid previous studies, as

there is no way directly measuring the relationship between returns and quality without a

factor accounted for quality. Without a clear picture of this imperative relationship it

would be very difficult to evaluate and pinpoint mutual fund’s performance accurately.

Our primary contribution is to the asset price theory as we have modified the FFM with

an additional QMJ factor, which is intuitive as it is driven by reversing engineering the

famous Gordon Growth Model, and it is also statistically consistent as AQR management

2

in their research paper demonstrated that superior risk adjusted returns can be registered

in retrospect.

The paper should also greatly benefit retail investors, mutual funds, hedge funds

and pension funds. Small retail investors should only invest in an actively managed

product if activism yields high benefits. If the performance of an actively managed

product is indifferent from the underlying benchmark retail investors should be reverting

to ETFs or other passive vehicles for cost saving. By incorporating this factor into their

analysis, they should be in a better position to their investment judgements. Institutional

buy side firms can also utilize this QMJ factor to guide through their management

selection process.

According to financial theory, quality of a business can be attributed to four broad

categories; profitability, growth prospect, Safety, and stocks pay-out.

Profitability: Profitability can be decomposed into two dimensions; profitability based

on accrual basis and cash flow basis. Profitability of a company indicates management’s

ability to efficiently use capital to create value to stakeholders.

Growth prospect: intuitively, good growth prospect should ultimately lead to high

profitability, and thus high quality.

Safety: High safety ultimately translates to the high stability and low volatility of a

business.

Stock Pay-out: Finally, higher and healthy stock pay-out should indicate manager’s

confidence of a business, and also reduces agency-problem. Therefore, high payout

should also lead to higher prices in the long term.

Our methodology is analogues to Jagadeesh and Titman’s (1993)’s approach as

we modified the FFM with an extra QMJ factor, and then applied factor model analysis to

3

evaluate mutual fund’s historical performance. If we can successfully establish the

relationship between returns and their exposure to the QMJ factor exposure, we can then

conclude that mutual fund managers are capable of selecting quality companies or

include quality in the investment process. In turn, this could establish some basis for

supporting the active mutual fund industry. Alternatively, we should be reverting to other

four explanations; 1) QMJ is too rudimentary and fails to capture other important quality

determinates, 2) mutual funds focus on other areas other than actively selecting quality

companies, 3) there could be other strategies that mutual fund employ to produce superior

returns, 4) we concur with the previous studies that active managers are incapable of

generating above benchmark returns.

Research interpretations

Since the AQR management clearly demonstrated (that’s one study, you need

more research to determine how successful this factor is.) that QMJ factor portfolio could

be used to generate high active returns in American stock market, and hence it should

help us to verify whether active managers attempt to outperform their relative

benchmarks by selecting quality stocks. In addition, the recent published paper,

“Digesting Anomalies” (2012), discovered a Q-Factor, similar to the QMJ factor but only

focuses on investment patterns and profitability, and it was subsequently confirmed by F.

Fama and Kenneth R. French in 2013 that applying this additional factor almost all the

unexplained average returns for individual portfolios are almost zero.

Despite our extensive statistical analysis, we could not find sufficient evidences to

support active investment through the lens of the QMJ factor’s loadings. There appear to

be a lot of inconsistences in terms of QMJ factor loadings across our analysis as some

4

results suggesting negative loading. Negative loadings imply that some funds actually

long low quality stocks while negatively exposing themselves to high quality ones.

Across the board, as we adding more systematic factors to our regressions, QMJ factor

does not seem to be very significant as 50% of the loadings become insignificant at 5%

level at. However, one interesting note is that the QMJ factor appears to correlate

negatively with the market and other conventional systematic risk factors, and thus

inclusion of it could potentially lower portfolio systematic risk. Furthermore, we

confirmed with previous studies that market factor is one of the most important sources to

explain investment returns as we added Market factor into our model, initially it

significant increased R-Squares by almost 30%-35% when we just added market to the

standalone QMJ model. Other factors; SMB, HML, and UMD appear to be significant

while the supporting evidence is not as strong as the market factor; SMB and HML

appear to be significant 60% to 70% of the time, and UMD appears to be significant 70%

to 80% of the time. This suggests that not all mutual funds in the US have a value and

small cap bias, and many funds appear to follow the Momentum approach by clinching

on or following previous winners. Although, we could not find sufficient evidences to

support active investment, we are still not in a position to repudiate the hypothesis that

active mutual fund can provide a better risk and reward profile for investors as other

techniques could be employed to generate better results. Furthermore, we could have

omitted other important factors that should be accounted for quality, and this could

jeopardize our analysis and interpretations. Furthermore, whether the original FFM is a

fair representation of the reality is still questionable, and thus the failure of not seeing

consistent results could be as result of other FFM factors.

5

The remainder of this paper is organized as following; section 2 will our research

methodology, in section 3 we will present all the descriptive statistics and data results,

section 4 will include our conclusion remarks, and finally section 5 will list all the

references we have in this paper.

Furthermore, we found an additional piece of interesting evidence that all the

regressions’ alphas appear to be statistically significant except a few. Alphas vary from -

0.04 to 0.055 monthly in the first QMJ only regression (Table 1), and when market factor

is included they are reduced systematically but becoming more significant (Table 2). As

we gradually include more systematic factors in our regressions, these alphas do not

reduce much and still very significant at 5% significance level. More importantly,

because we rank our portfolios according to their lagged performance, the better than

ranking the better the average alpha, while the previously worst 50% performing funds

tend to have a negative alpha. There are about 50% of the portfolios’ alphas in positive

and the other 50% in negative. Moreover, the average alpha across these 10 portfolios of

funds is almost zero in every set of regressions except the first set where our regressions

only include the QMJ factor. This could possibly imply that while collectively there are

indifferent from their benchmarks (not outperforming as a group), top groups of funds

can generate positive alphas for the reasons yet to determine. It is important to note that

some managers claim they can systematically time the market, and some managers can

use other unconventional investment techniques to outperform the market. If quality

selection process cannot fully explain these alphas, they could be a result of managers’

unique investment skills. Alternatively, perhaps our QMJ factor is too rudimentary to

6

capture all the quality metrics, for example industry competition, supplier concentration,

buyer concentration are not included in our QMJ factor.

7

2: Previous Literature

.

2.1 Asset Pricing

The essence of asset pricing is to explain how investors evaluate risks, and in turn

how they determine what risk premium to demand collectively. Therefore, the risk

premium or implied return determines the correct asset prices. Historically, US equity

market has returned investors on average a whopping 9%, only 10% of that 9% is

attributed to interest rates and the rest is a function of equity risk premium. Therefore, it

is no surprise that modern financial economists and practitioners have spent a great deal

of their time in studying what drive risk premium. The modern asset pricing began with

the work of Markowitz (1959), he suggested that all investors allocate their capital

rationally and mean variance efficiently. The notion of Mean-Variance portfolio was

further developed in the 1960s by William Sharpe (1964), Jack Treynor (1962), and John

Lintner and Jan Mossin (1965 -1966). As a result, CAPM famously emerged due to its

strong theoretical structure. The simplicity of CAPM suggests that only one factor is

required to explain all asset returns; that is the market factor. In other words, the market

factor is the only source of uncertainty beside risk free rate. However, overwhelming

evidences seemed to disprove CAPM despite it is widely applied as it has failed to

explain asset returns and achieve statistical significance. (Black, Jensen and Scholes

(1972) made one of the earliest empirical studies of CAPM, unfortunately, their

8

estimations of slope and intercept are vastly different from the CAPM predictions)

Perhaps, it is the stringent economic assumptions underlying CAPM invalidate it largely.

As a CAPM failed to fit the empirical data, other theories were also developed which

include APT by Ross (1976), Fama French Model (1992) and Supply-side

Macroeconomic model by Chen, Roll and Ross (1986). Apart from arguing whether the

proxy of market portfolio is efficient, there are two additional branches of studies attempt

to explain why reality is drastically different from theories would suggest; 1) behaviour

finance argues that there are behaviour factors we failed to include in our models and

some are indeed deemed to be irrational in the eyes of orthodox school of thoughts, and

2) there are other systematic risk factors our CAPM misses. In the traditional view of

economics and finance, irrational factors are not important in solving equilibrium models,

assumed random and thus non-systematic. However, reality suggests otherwise, human

behaviours exhibit irrational patterns, and thus the efficient market hypothesis partially

depends on full rationality is indeed questionable.

As famously summarized by the Former Federal Reserve Chairman, Alan

Greenspan, in his book of The Age of Turbulence; “But after several years of closely

studying the manifestations of animal spirits during times of severe crisis, I have come to

believe that people, especially during periods of extreme economic stress, act in ways

that are more predictable than economists have traditionally understood. More important,

such behaviours are measurable and should be an integral part of economic forecasting

and economic policymaking. Spirits, it turns out, display consistencies that can help

economists identify emerging price bubbles in equities, commodities, and exchange rates

-- and can even help them anticipate the economic consequences of those assets’ ultimate

collapse and recovery.” Moreover, he continues; “From the perspective of a forecaster,

9

the issue is not whether behaviour is rational but whether it is sufficiently repetitive and

systematic to be numerically measured and predicted.”

Financial economists supporting the view of multi factors model think that CAPM

has excluded other important systematic risk factors. Fama French (1993) discovered two

additional factors that should be included to explain asset returns; value factor and size

factor. Since then more factors have been introduced to make slight adjustments to the

Fama and French three-factor model. In 1993, Jegadeesh and Titman have discovered

that stocks performed well in the past outperformed stocks with past poor performance;

Momentum effect. The momentum effect tends to imply that market is under reacting to

information systematically. Despite the weak evidences for rational explanations, the

Fama and French three factor model with high R square failed to explain the effect of

momentum. On the other hand, Lakonishok, Shleifer and Vishny (1994) suggest that high

returns are a consequence of investors’ overreactions. Furthermore, they indicate that

investors tend to ignore stocks with high B/M, and thus under researched by analysts. In

2009 Asbess, Moskowitz and Pedersen provide evidence that both Momentum and Value

strategies are successful when applying in a range of asset classes; currencies,

commodities, and bonds. In addition, a more recent study carried out by Kewei Hou,

Chen Xue, and Lu Zhang, published in 2012, “Digesting Anomalies: An Investment

Approach,” suggested a new factor model that attempts to explain many of the anomalies

that none of the previous models can do a good job to explain. The additional factors are

investment and profitability; it is called “The q-factor Model”. The major difference

between this new approach and the previous ones is the introduction of two new beta

dimensions: investment and profitability factors, which are widely accepted by the

investment committee in terms of using it to judge stock performance. In the Fama &

10

French 2013 paper, five –Factor Asset pricing model, they used a set of empirical tests to

verify if adding the profitability and investment patterns factor to their existing three

factor model can yield a model that is superior to the old factor models, and they noted

that “While the five- factor model does not improve the description of average returns of

the four factor model that drops the HML, the five factor model may be a better choice in

application. For example, through captured by exposures to other factors, there is a large

value premium in average returns that is often targeted by money managers”

Furthermore, they also state that “Unexplained average returns for individual portfolios

are almost all close to zero.” Therefore, there are still more questions need to be

answered before any conclusions can be made. Following the footsteps of these people,

and using a new paper published by the AQR Capital Management as the foundation of

our thesis, “Quality Minus Junk”, we attempt to provide an update of the paper published

by its original authors by using data including 2015. In the “Quality Minus Junk” study,

quality factor is further divided into four dimensions to further decompose the effects of

the quality factor. Among the four quality factors, profitability is an important one

although defined differently from the paper, “Digesting Anomalies: An Investment

Approach,” we came up with evidences suggesting that this quality factor is important,

and can earn significant higher risk adjusted returns with information ratio above one.

In this paper we will illustrate the logic behind the QMJ factor, and use this factor

to modify the Fama & French model as we try to evaluate the US mutual fund industry

performance in relation to the QMJ factor over the past 15 years.

11

2.2 Mutual Funds’ Performance

In theory, active investors should perform differently from their benchmarks in

order to achieve alphas. Economic theory suggest that active investors through buying

and selling securities and sending pricing signals should enhance business efficiency

overall, and thus growing the economic pie and obtain excess returns. However, it is

observed by the investment world that alphas are difficult to get. The overall academic

consensus is mixed with regard to the merits of mutual fund industry, but slightly skewed

towards the notion that it is better off buying indexed funds as mutual funds’ high

management fees erode away any rare excess returns. Mark M. Carhart (1997), in their

paper, on persistence in Mutual Fund Performance, suggest that common factors in stock

returns and persistent differences in mutual fund expenses and transaction costs explain

almost all the predictability in mutual fund returns. Classically, evidences from Jensen

(1969) suggest that subsequent good performance does not follows previous superior

performance, and more importantly, their evidences pointing towards the conclusion that

those superior returns are mainly a function of luck. Several other subsequent research

articles (e.g. Malkiel, 1995; Gruber, 1996; Carhart, 1997) also reconfirmed Jensen’s

findings. In light of the recent financial crisis, more studies have came out to demonstrate

worse performance relative to their benchmarks by active funds during market downturns

(e.g. Souza and Lynch, 2012; Pfeiffer and Evensky, 2012) More recently, an article

published by the investment practitioners side of the business (Vanguard, 2009) discovers

very little evidence in support of superior active management performance during market

turmoil and stat that “in fact, active managers have not consistently delivered superior

performance relative to a benchmark during such periods.” Furthermore, Vanguard in

2009 shown that active fund managers failed to outperform broader stock market 4 out of

12

7 bear markets. However, reality is not always so black and white, particularly in the field

of finance and economics a subset of social science, there are as much supporting active

investment evidences as non-supporting evidences. For instances, using a sample of

quarterly portfolio data, Grinblatt and Titman (1989) present evidences to support mutual

fund positive abnormal performance especially in two categories; growth and aggressive

growth funds. Later studies (e.g. Grinblatt and Titman, 1993; Grinblatt, Titman, and

Wermers, 1995; Wermers, 1997) also suggested superior performance by actively

managed mutual funds. However, it is worthwhile to notice that most of their findings in

support of alphas are a result of using gross returns rather than net returns since our focus

is on whether as an average investor should use mutual funds as the core portfolio

building block. In addition, Hendricks, Patel, and Zeckhauser (1993), Goetzmann and

Ibbotson (1994), Brown and Goetzmann (1995) also find strong evidences of persistence

in mutual fund performance over one to three year horizon, and ultimately attributed the

persistence to “Hot Hand” or common investment effect. In the view of longer term

persistence, Elton, Gruber, Das, Hlavka (1993), and Blake (1996) show that superior

performance should be a result of stock picking skills and manager’s information value.

In particular, with respect to Hendricks, Patel, and Zeckhauser’s (1993) hot hand effect,

Mark M. Carhart (1997) present evidences to suggest that most can be attributed to

Jagadeesh and Titman’s (1993) one year momentum in stock returns. Furthermore, they

stat that “ funds that earn higher one year returns do so not because fund managers

successfully follow momentum strategies, but because some mutual funds just happen by

chance to hold relatively larger positions in last year’s winning stocks.” Explanations as

why active mutual funds tend to underperform ranging from mean reverting evidences to

over diversified effects from mutual fund industry. In Shawky and Smith (2005), they

13

suggest an optimal point of holdings and beyond which value would be destroyed as a

consequence. This finding can be traced to several corporate finance studies that suggest

business diversification result in value reductions on average. (E.g. Lang and Stulz, 1994)

However, Sapp and Yan (2008) show that even focused funds tend to destroy values by

underperforming. It is important to notice that not all evidences in the real worlds are

repudiating active investment strategies.

Furthermore, much of the previous works related to mutual fund performance

were carried out from the perspective of FFM and its closely related variations. We need

a fundamental factor to measure active returns as majority of professional money

managers claim that they make their investment selections based on the fundamental

approach. The essence of the approach is to identify quality investments, which are

undervalued currently. Therefore, we think the additional QMJ factor based on the four

major quality factors, will capture this fundamental relationship.

14

3: Data and Methodology

In this thesis, portfolios of mutual funds (dependent variable) formed on lagged 1

year return is regressed to systematic risk factors (independent variables) to see if mutual

funds can provide persistent excess return. Thus, we used two sets of data in this thesis to

perform statistic test: Mutual Funds Data and Factors’ Data.

3.1 Factors’ data and Methodology

The data for factors used in this thesis are from the AQR’S homepage. It includes

the three Fama & French four factors, market risk premium, SMB, HML and UMD;

quality minus junk factors, QMJ; as well as the risk free rate with the one month US

Treasury bill as a proxy. Since we can only obtain mutual funds data from U.S. market,

we only used U.S. factor data from AQR’s dataset. Please see table 7 in appendix for a

summary of factors, as well as correlation between them.

All factor portfolios construction follows Fama and French (1992, 1993, and 1996)

and Asness and Frazzini (2013) and Asness, Frazzini and Pedersen (2013).

3.1.1 Fama and French Four Factors

The Market factor MKT is the value-weighted return on all available stocks

minus the one-month Treasury bill rate.

The size, value and momentum factors are constructed using six value-

weighted portfolios formed on size and book –to-market and 1-year return. At the end of

each calendar month, stocks are assigned to two size-sorted portfolios based on their

15

market capitalization. The size breakpoint is the median NYSE market equity. AQR use

conditional sorts, first sorting on size, then on the second variable and rebalance portfolio

monthly to maintain value weights. They believe conditional sorts, which slightly

different from Fama and French (1992, 1993, and 1996)’s independent sorts, ensure a

balanced number of securities in each portfolio.

The size factor SMB is the average return on the 3 small portfolios minus the

average return on the 3 big portfolios: SMB = 1/3(small value + small neutral + small

growth) – 1/3(Big value + Big Neutral + Big growth).

The value factor HML follows Fama and French (1992, 1993, and 1996(. HML is

the average return on the two value portfolios minus the average return on the two growth

portfolios: HML = 1/2(small value + Big value) – 1/2(small growth + Big growth). To

compute book to market ratios, AQR scale book equity (BE) by the total market value of

equity (ME) at fiscal year-end.

The momentum factor UMD is the average return on the two high return

portfolios minus the average return on the two low return portfolios: UMD = ½(small

High + Big High) – ½(small Low + Big Low).

Each factor portfolios are value weighted; breakpoints are refreshed every month

and rebalanced every month to maintain value weights.

3.1.2 QMJ factors

As the Quality Minus Junk Factor (QMJ) is the new factor in this thesis used to

test mutual funds performance, we describe its data sources and the methodology for

constructing quality measures in more details.

16

Pricing and accounting data are from the union of the CRSP tape and the

Compustat/XpressFeed Global database. The U.S. data include all available common

stocks in the merged CRSP/XpressFeed data. All portfolio returns are in USD and do not

include any currency hedging. Excess returns are above the U.S. Treasury bill rate.

Quality Score

A variety of quality measures are used to identifying stocks of profitable, stable,

safe and high payout companies. To avoid data mining, a broad set of measures are

employed by AQR for each aspect of quality and average them to compute four

composite proxies: Profitability, Growth, Safety and Payout. Then these four proxies of

quality are averaged to arrive a single quality score.

Profitability is measured by gross profits over assets (GPOA), return on equity

(ROE), return on assets (ROA), cash flow over assets (CFOA), gross margin (GMAR),

and the fraction of earnings composed of cash (i.e. low accruals, ACC). To combine each

measure, they must be standardized, which is done by converting each variable into ranks

and then to get it z-score.

More formally, explained by AQR “let x be the variable of interest and r be the

vector of ranks, Ri = Rank(Xi). Then the z-score of x is given by Z(x)=Zx=(r-Ur)/Dr,

where Ur and Dr are the cross sectional mean and standard deviation of r. “

Thus, Profitability score is the average of the individual z-scores:

Profitability = Z(Zola + Zroe + Zroa + Zcfoa + Zgmar +Zacc)

In a same way, Growth is measured as the five-year prior growth in profitability,

then averaged to get a Growth proxy.

Growth = Z (ZΔgpoa + ZΔroe + ZΔroa + ZΔcfoa + ZΔgmar +ZΔacc)

17

Safty is defined by low beta(BAB), low volatility(IVOL), low leverage(LEV), low

bankruptcy risk (O-score and Z-core) and low ROE volatility (EVOL):

Safety = Z(Zbab +Zivol +Zlev + Zo + Zz +Zevol)

Payout is defined by Equity and debt net issuance (EISS, DISS) and total net

payout over profit (NPOP):

Payout = Z (Zeiss +Zdiss +Znpop)

Last, four quality proxies are combined into one quality score by averaging them:

Quality = Z(Zprofitablility + Zgrowth + Zsafety + Zpayout)

Once having the quality score, quality–minus-junk factors (QMJ factors) can be

constructed by following Fama and French (1992, 1993, and 1996) and Asness and

Frazzini (2013). By intersecting of six value-weighted portfolios formed on size and

quality, stocks are assign to two size-sorted portfolios monthly based on their market

capitalization. Size breakpoint is the median NYSE market equity. AQR use conditional

sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed and

rebalanced monthly. The QMJ factor return is

QMJ = 1/2 (Small Quality + Big Quality) – ½(Small Junk + Big Junk)

= 1/2 (Small Quality - Small Junk) + ½(Big Quality - Big Junk)

3.2 Mutual Funds’ Data and Methodology

The data for mutual funds returns used in this thesis is from Center for Research in

Security Prices Data base (CRSP). The programs Access, Excel and Matlab are used to

clean and analyze the data. We choose to keep only the observations that are relevant to

our research. Since previous research has covered periods before 2000, in this paper, the

18

focus is for the period year 2000 to year 2014, thus observations before year 2000 are

excluded and only data covering monthly value weighted returns are used. In addition, as

result of availability, mutual funds data is from U.S. market only.

3.2.1 Cleaning data

To filter out outlier funds, only data for funds with net Asset value per share >0

and total net Asset value >100k is downloaded from CRSP mutual funds database. Since

only pure equity funds are relevant, all funds with any debt holding are eliminated from

sample data; funds with less than 10 percent of other assets is allowed and included in

sample data to obtain enough observations. Next, we only keep funds with complete

observations from 2000 to 2014 (180 observations) in the sample. Thus, funds closed or

new commenced during the period are eliminated, as well as those with errors in return

data. The result is 517 funds. Last, I further eliminated outliers that have monthly returns

of top 2% or bottom 2% of all. The result is our sample covering 500 funds in U.S.

Market, 180 month of observation for each.

3.2.2 One year lagged return

Our question is if Mutual funds’ performance is persistent, that is, if one is a

winner this year, if it is still a winner a year later. Thus, for each month, the funds’ return

data first subtract risk free rate for the month to get their risk premium and then sorted

based on this risk premium from low to high. Next, based on this ranking, funds’ 1 year

lagged return is associated. As result of lagged return, we now have one year less of

observations, which come to 84,000 of funds monthly return observations.

To make our sample data ready for fixed effects model, each fund’s monthly

return subtracts its mean monthly return.

19

3.2.3 Assign funds to 10 portfolios

Based on classic empirical testing approach, 10 portfolio of mutual funds are

formed. Mutual funds are sorted every month from January 1, 2000 to Dec 31, 2013 into

deciles portfolios based on their previous calendar year’s return. The portfolios are

equally weighted monthly. Funds with the highest past one-year return comprise decile 1

portfolio and funds with the lowest comprise decile 10 portfolio.

Now, we have our mutual funds data ready for testing.

3.3 Main Statistical Test

Mutual Funds’ returns are strongly co-moved together. The fundamental source of

the co-movement is hard to observe, not to mention to be measured. (Kritzman, 1993).

Factor models are very useful in a situation where a few unobservable sources of

systematic risk affect many random variables. The Fama and French four-factor model

controls portfolios risk by managing its exposure to 4 common sources. In this thesis, we

add one more common source of risk, quality. By discovering sources of risk, we might

be able to control risk better. On the other hand, by examining funds’ risk exposure; we

can see how well funds perform in term of risk exposure; if adding more risk factor could

help to explain funds’ performance.

The method used in this thesis to analysis panel data for mutual funds’

performance is by using fixed effect model. The method has been widely used to evaluate

linear factor pricing models with panel data. We specify the sources of return co-

variation, and then try to confirm whether these sources do indeed correspond to

difference in return.

Fixed effect

20

In econometrics, a fixed effects model represents the observed quantities in terms

of explanatory variables that are treated as if the quantities were non-random. Such

models assist in controlling for unobserved heterogeneity when this heterogeneity is

constant over time and correlated with independent variables. This constant can be

removed from the data through differencing. Since it is reasonable to assume funds’

return (dependent variable) is not random correlated with systematic risk factors

(independent variables), we employ fixed effects models here. In panel data analysis

here, we impose time independent effects for each entity that are possibly correlated with

the repressors.

21

4: Results

Regression results for the 10 mutual fund portfolios can be seen in table 1, 2, 3, 4,

5, and 6. Regression results are from the past 15-year’s monthly data from 2000 to 2014.

We conduct our analysis by using monthly US Treasury bill rate as the model risk free

rate. We perform our analysis without any currency exchange adjustment as we assume

the perspective of an US-Dollar investor.

Table 1 presents the regression results obtained by regressing each portfolio’s

returns with only the QMJ factor alone. Surprisingly, QMJ appears to be negatively

correlated with portfolio’s returns and significant. While R-square is quite low hovering

around 50%, this suggests that QMJ alone is not sufficient to explain portfolios’ return

variations and there should be other factors to explain their return variations. Alphas are

mostly significant but with no sign of any consistence as 40% are in the negative territory

and the other 60% are in the positive zone.

We combine the Market factor with QMJ in our regression analysis and present

results in Table 2. Lo and behold, R-squares are significant higher than table 1’s results

by large margins almost by 40%, which could imply that the market-factor heavily

influences these mutual funds on average. Average R-Square is around 92%. We plotted

these two series of R-square in Graph 1, and as we can clearly observe that R-squares

with just QMJ are dominated largely by the series that includes both the market and QMJ

factor. In addition, all the market factor loadings are hovering around 1 plus and minus

0.15 and significant. This suggests strong evidence to support the market factor as it

22

appears to be consistent, and all mutual funds have a positive exposure to market factor

risk.

It is worth to mention that the QMJ factor appears to correlate less negatively with

mutual fund portfolio’s returns after including market factor in the regression analysis.

Graph 2 shows that our QMJ coefficients with the Market factor are less negative than

the QMJ coefficients without the market factor. This evidence suggests that there could

be some degree of fixed effect as the market factor and the QMJ factor could be

negatively related with each other. This finding is consistent with AQR Management

results that QMJ factor tends to be negatively correlated with other systematic factors.

However, assuming a significance level of 0.05, QMJ factor appears to be less significant

as 7 out of the 10 portfolio’s P-value are above the critical level, and this led us to accept

the Null hypothesis that QMJ’s coefficient is indifferent from zero.

Table 3 shows that mutual funds in the US do not appear to be strongly tilted

towards either Small Cap or large Cap, and either value or growth style. We run a

standard FFM Three-Factor-Model for each of the 10 portfolios and present our results in

Table 3. At 5% significance level, there are only 5 portfolios with positive exposure to

SMB and also statistically significant. At 5% significance level, there are 6 portfolios

with positive exposure to HML factor and also statistically significant. While the

consistence is slightly better for HML factor, we still do not have sufficient evidence to

conclude that US mutual funds tend to be more value orientated. Furthermore, R-squares

only have been marginally improved comparing with the results generated by the simple

Market + QMJ regression model.

Table 4 presents the regression results of FFM Three-Factor-Model plus the QMJ

factor. R-Squares are somewhat indifferent from the simple Three-Factor-Model’s

23

results, while this regression has slightly changed our impression of SMB factor, as 70%

of the coefficients are now significant. This implies that QMJ cannot explain fund returns

as other variables should be used. Majority of QMJ coefficients have turned to positive as

Table 4 shows. Again, this shows that QMJ factor is somehow different from the

systematic factors as shown in the Quality-Minus-Junk paper from AQR Management.

Table 5 shows the regression results after including the Momentum factor (UMD). We

refer this as the Fama and French Four-Factor-Model. Including UMD in our analysis

does not dramatically alter the regression results from Table 4. R-squares are quite alike

the R-Squares generated from the Standard Three Factor Model. This implies that

marginal explanatory power of the momentum factor is very low. However, 80% of

UMD are significant and positive. This confirms with previous studies to suggest that

mutual funds tend to in previous winners either passively or actively.

Table 6 shows the results of FFM Four-Factor-Model plus QMJ factor. While R-

square stay relatively indifferent from the standard Four-Factor-Model alone, both UMD

and SMB factor are significant as 70% of SMB and 80% of UMD factor loadings are

significant at 5% significance level. This find is consistently with our understanding of

the SMB factor’s size effect; when comparing stocks of similar quality, small stock

should outperform large stocks on average.

Table 1, 2, 3, 4, 5, 6, second column shows their respective regression’s alphas. It

is evident that they are almost all significant except one in the first table at 5%

significance level. As we gradually increase more factors into the regression, their alphas

systematically are reduced as shown in Graph 3. When including the Market Factor

alphas are all reduced by a quite constant amount 0.075 approximately, this means that

the ability of the market to explain return variations is significant and strong. As we

24

added systematic factors into regression analysis we see that the alphas start to level out

(Graph 3), with 50% in positive and rest in negative. These alphas are all significant and

consistent with their performance rankings; the best performing funds tend to register

higher positive alphas. This suggests a strong positive correlation between alphas and

their performance rankings. Furthermore, these alphas demonstrate we have some

evidence to believe that some funds are capable of generating above market returns due

to unique reasons cannot be explained by the systematic factors and QMJ factor.

Collectively, their average alpha appears to be close to zero, this confirms with previous

studies that mutual fund industry as a group cannot outperform the market, but the high-

ranking funds that can generate positive alphas perhaps at the expense of other active

fund’s underperformance as this could be a zero sum game or other reasons require

further study.

Results conclusion

There is no sufficient evidence to suggest that mutual funds focus on quality

investment as a mean to achieve excessive returns suggested by our regression results,

while QMJ factor tend to behave differently from most market systematic factors. As

suggested by ARQ’S QMJ paper and our regression results, QMJ appears to correlate

negatively with the market factor. There is weak evidence that some mutual fund focus

on small cap and value stocks. Consistent with both FFM and CAPM, it appears that the

Market Factor is one of the most important factors in explaining mutual fund returns.

Other systematic factors while seem to be significant cannot materially improve R-

square. Finally, we found quite strong evidence to suggest that mutual fund industry as a

whole tends to follow previous winners, but it is unknown to us whether they do it

25

actively or passively. Moreover, evidence suggests that there is a strong positive

correlation between fund’s alphas and their corresponding rankings. Therefore, we

believe that some funds are capable of generating positive alphas for specific reasons we

do not know as our factors cannot explain this situation, while these returns cannot be

explained my our quality factor. (QMJ)

26

5: Implications and Conclusions

In this paper we attempt to bridge Asset Pricing Theory that primarily focus on

systematic factors with fundamental investment theory that focuses on actively scooping

quality companies to achieve outperformance. Our goal is to use the integrated model to

explain US active mutual fund performance.

conventional wisdom in the finance industry tells us that outperformance can be

achieved by selecting quality investments at a reasonable low price. However, to the

extent of what quality encompasses is quite blurry as different investors define quality

slightly different depending upon their unique set of beliefs. It seems reasonable to

assume that if a company grows at robust and sustainable rates, operates at high and

steady profit margins, and disburses cash handsomely to its shareholders, the company is

generally a quality company relatively to its peers. More importantly, these metrics are

quantifiable with a reasonably degree of assurance. Therefore, QMJ factor is selected to

rank companies as it encompasses all four quality metrics; safety, profitability, growth

prospect, and pay-out ratio. If else equal, high quality firms should have higher scaled

prices. AQR Management indicates that it is consistent with market efficiency theory;

high quality firms do exhibit higher prices on average. However, the explanatory power

of quality on prices is low, leaving the majority of cross sectional dispersion in scaled

prices unexplained. Therefore, high quality firms exhibit high risk-adjusted returns. A

quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-

quality stocks earns significant risk-adjusted returns with an information ratio above 1 in

27

the U.S. and globally across 24 countries. Therefore, we believe that the QMJ factor

includes the necessary information for us to test mutual fund performance.

Our results present a puzzle for asset pricing and mutual fund performance, as we

believe that we are not the first one to find conflicting evidence with regard to mutual

fund attributions. Despite our high confidence in the QMJ factor, there is no consistent

evidence to conclude that active managers as a whole tilted towards quality companies, as

some QMJ factor loadings in our regression models are positive while others are

negative, through most of these loadings are insignificant.

There are five major explanations to our findings.

1) Quality is differently defined in reality or the QMJ factor does not include all-

important metrics pertaining to quality. Future studies should try to refine QMJ

factor to include unique metrics pertaining to quality, and look for important

factors that we have not yet quantified; industry competition, supplier and

customer concentration, barrier of entry, and so called “Steve Job Effect”.

2) Mutual fund industry uses a different set of techniques to capture excessive

returns. It may be useful to re-categorize them according to their investment

mandates, as each style is quite different from others.

3) Sample selection problem as a result of including all US available mutual funds.

Some mutual funds can be self-proclaimed active but in fact passive. Therefore, it

is necessary to separate real-active funds from the self-proclaimed active funds if

one would like to find out the truth behind active mutual funds.

28

4) Collectively as a whole, the industry cannot select quality companies consistently

but individual funds could, but they are buried beneath the average numbers. As

we have mentioned in our literature review that the best active funds tend to be

more consistent in terms of generating superior performance, but collectively as a

group the negative ones might have neutralized the superior results. Mutual fund

industry collectively represents a significant portion of all market assets, and as

they are competing with each other, they skills would have been neutralized as a

whole and reverting back towards benchmark returns.

5) QMJ and FFM may not fit well with each other, as the latter is a factor model

includes mostly systematic factors. Therefore, QMJ factor should be

concatenated with a different model.

29

6: Appendix

Table 1

10 portfolios’ monthly returns against QMJ factor

Table 1 ALPHA P-Value QMJ P-Value R-Square Adjusted

P1 -0.034988 0.000000 -1.222320 0.000000 0.562598

P2 -0.014433 0.000000 -1.113460 0.000000 0.599680

P3 -0.006345 0.011002 -1.058786 0.000000 0.580683

P4 -0.000244 0.920331 -1.022867 0.000000 0.625683

P5 0.005243 0.030859 -0.993440 0.000000 0.599538

P6 0.010332 0.000023 -0.980911 0.000000 0.588692

P7 0.015885 0.000000 -0.977818 0.000000 0.570422

P8 0.022416 0.000000 -0.994747 0.000000 0.585677

P9 0.031844 0.000000 -1.047365 0.000000 0.592899

P10 0.054883 0.000000 -1.125732 0.000000 0.561942

30

Table 2

10 portfolios’ monthly returns against QMJ factor and Market Factor

Table 2 ALPHA P-Value MKT P-Value

P1 -0.043170 0.000000 1.048539 0.000000

P2 -0.022404 0.000000 1.021452 0.000000

P3 -0.014233 0.000000 1.010902 0.000000

P4 -0.008143 0.000000 1.012239 0.000000

P5 -0.002620 0.000007 1.007635 0.000000

P6 0.002617 0.000023 0.988619 0.000000

P7 0.008377 0.000000 0.962187 0.000000

P8 0.015142 0.000000 0.932140 0.000000

P9 0.024984 0.000000 0.879053 0.000000

P10 0.048694 0.000000 0.793124 0.000000

QMJ P-Value R-Square Adjusted

-0.134022 0.066483 0.822439

-0.053275 0.237204 0.914906

-0.009552 0.774160 0.938525

0.027755 0.302918 0.965023

0.052404 0.033122 0.978742

0.045196 0.083448 0.959460

0.020855 0.511159 0.948347

-0.027261 0.515677 0.949850

-0.134979 0.025230 0.920007

-0.302534 0.001191 0.855993

31

Table 3

10 portfolios’ monthly returns against Fama-French-Three-Factor

Table 3 ALPHA P-Value MKT P-Value

P1 -0.043822 0.000000 1.122171 0.000000

P2 -0.022914 0.000000 1.044742 0.000000

P3 -0.014543 0.000000 1.012402 0.000000

P4 -0.008303 0.000000 0.994042 0.000000

P5 -0.002716 0.000001 0.976711 0.000000

P6 0.002369 0.000034 0.955610 0.000000

P7 0.007806 0.000000 0.932923 0.000000

P8 0.014036 0.000000 0.915942 0.000000

P9 0.022983 0.000000 0.895639 0.000000

P10 0.045654 0.000000 0.864353 0.000000

SMB P-Value HML P-Value R-Square Adjusted

-0.013631 0.831000 -0.031881 0.581653 0.825431

0.032992 0.400781 0.024395 0.492568 0.916552

0.030416 0.290365 0.043412 0.096431 0.939070

0.033617 0.142884 0.061289 0.003472 0.965582

0.037100 0.070256 0.081181 0.000019 0.979108

0.065722 0.002315 0.087827 0.000009 0.960450

0.111161 0.000020 0.098950 0.000028 0.948284

0.174136 0.000000 0.115080 0.000180 0.952610

0.281529 0.000000 0.095815 0.029350 0.923030

0.411341 0.000000 0.000867 0.989985 0.855473

32

Table 4

10 portfolios’ monthly returns against Fama-French-Three-Factor plus QMJ

Table 4 alpha P-Value MKT P-Value

P1 -0.042347 0.000000 1.035248 0.000000

P2 -0.022542 0.000000 1.022798 0.000000

P3 -0.014593 0.000000 1.015351 0.000000

P4 -0.008748 0.000000 1.020273 0.000000

P5 -0.003420 0.000000 1.018265 0.000000

P6 0.001555 0.007549 1.003626 0.000000

P7 0.006956 0.000000 0.983087 0.000000

P8 0.013288 0.000000 0.960030 0.000000

P9 0.022624 0.000000 0.916825 0.000000

P10 0.046070 0.000000 0.839878 0.000000

SMB P-Value HML P-Value

-0.107299 0.154881 -0.030707 0.591234

0.009345 0.841645 0.024691 0.487523

0.033595 0.328392 0.043373 0.097676

0.061883 0.023187 0.060935 0.003418

0.081879 0.000636 0.080620 0.000012

0.117465 0.000003 0.087179 0.000005

0.165218 0.000000 0.098273 0.000019

0.221645 0.000000 0.114484 0.000165

0.304359 0.000000 0.095529 0.030059

0.384966 0.000038 0.001198 0.986198

QMJ P-Value R-Square Adjusted

-0.199069 0.023076 0.824947

-0.050257 0.353306 0.916119

0.006756 0.864850 0.939122

0.060073 0.056109 0.965462

0.095166 0.000597 0.979563

0.109967 0.000136 0.960980

0.114884 0.000890 0.949603

0.100968 0.026905 0.953244

0.048520 0.466324 0.922565

-0.056053 0.594910 0.855769

33

Table 5

10 portfolios’ monthly returns against Fama-French-Four-Factor

Table 5 ALPHA P-Value MKT P-Value

P1 -0.044309 0.000000 1.166663 0.000000

P2 -0.023212 0.000000 1.071974 0.000000

P3 -0.014815 0.000000 1.037277 0.000000

P4 -0.008535 0.000000 1.015230 0.000000

P5 -0.002918 0.000000 0.995144 0.000000

P6 0.002202 0.000075 0.970856 0.000000

P7 0.007629 0.000000 0.949085 0.000000

P8 0.013845 0.000000 0.933334 0.000000

P9 0.022769 0.000000 0.915167 0.000000

P10 0.045419 0.000000 0.885828 0.000000

SMB P-Value HML P-Value

-0.003358 0.956919 -0.018788 0.738900

0.039279 0.304389 0.032408 0.349889

0.036159 0.188987 0.050732 0.042803

0.038509 0.077373 0.067525 0.000738

0.041356 0.034291 0.086605 0.000002

0.069242 0.000981 0.092313 0.000002

0.114893 0.000007 0.103706 0.000008

0.178151 0.000000 0.120197 0.000078

0.286038 0.000000 0.101562 0.020400

0.416299 0.000000 0.007187 0.917202

UMD P-Value R-Square Adjusted

0.102521 0.000975 0.824431

0.062749 0.001018 0.919640

0.057318 0.000035 0.940629

0.048823 0.000009 0.965981

0.042474 0.000015 0.980414

0.035130 0.000692 0.967487

0.037241 0.002678 0.952777

0.040074 0.013930 0.960893

0.044998 0.057860 0.934696

0.049483 0.188567 0.865533

34

Table 6

10 portfolios’ monthly returns against Fama-French-Three-Factor plus

Momentum factor & QMJ

Table 6 ALPHA P-Value MKT P-Value SMB P-Value

P1 -0.042626 0.000000 1.068804 0.000000 -0.112162 0.123839

P2 -0.022705 0.000000 1.042484 0.000000 0.006491 0.886216

P3 -0.014737 0.000000 1.032708 0.000000 0.031079 0.343674

P4 -0.008865 0.000000 1.034411 0.000000 0.059834 0.021096

P5 -0.003518 0.000000 1.030054 0.000000 0.080170 0.000474

P6 0.001477 0.009305 1.013005 0.000000 0.116106 0.000002

P7 0.006873 0.000000 0.993049 0.000000 0.163774 0.000000

P8 0.013197 0.000000 0.971019 0.000000 0.220052 0.000000

P9 0.022515 0.000000 0.929936 0.000000 0.302459 0.000000

P10 0.045939 0.000000 0.855598 0.000000 0.382688 0.000040

HML P-Value UMD P-Value

-0.016249 0.769026 0.111639 0.000290

0.033174 0.337663 0.065496 0.000645

0.050851 0.042901 0.057743 0.000036

0.067027 0.000773 0.047036 0.000019

0.085699 0.000001 0.039221 0.000044

0.091220 0.000001 0.031203 0.001895

0.102565 0.000006 0.033145 0.006376

0.119220 0.000078 0.036562 0.024313

0.101179 0.021157 0.043622 0.068060

0.007971 0.908356 0.052300 0.167937

QMJ P-Value R-Square Adjusted

-0.233179 0.006323 0.823869

-0.070268 0.184028 0.920472

-0.010887 0.775234 0.940272

0.045702 0.128217 0.966233

0.083183 0.001753 0.980386

0.100433 0.000369 0.967342

0.104757 0.002103 0.952668

0.089797 0.047471 0.960713

0.035192 0.596850 0.936995

-0.072033 0.495988 0.871812

35

Table 7

Factors’ Summary and Correlations

Factor Portfolio

Monthly Excess Return Stud Dev

t-stat for Mean =0 MKT SMB HML UMD QMJ

MKT 0.47% 4.62% 1.317 1

SMB 0.42% 2.51% 2.157 0.3976 1

HML 0.22% 2.56% 1.137 -0.0014 0.0288 1

UMD 0.16% 5.46% 0.379 -0.4776 -0.4080 0.1370 1

QMJ 0.30% 3.02% 1.284 -0.7926 -0.5307 -0.0977 0.6090 1

36

Graph 1

Plotting two sets of regressions QMJ factor loading; 10 portfolios’ returns against

QMJ, and 10 portfolios’ against QMJ and Market factor.

-1.400000

-1.200000

-1.000000

-0.800000

-0.600000

-0.400000

-0.200000

0.000000

0.200000

1 2 3 4 5 6 7 8 9 10

QMJ Coefficient

QMJ & MKT Coefficient

37

Graph 2

Plotting each regression’s R-squares, two sets of regressions’ R-Squares are

plotted; 10 portfolios’ returns against QMJ, and 10 portfolios’ against QMJ and

Market factor.

0.000000

0.200000

0.400000

0.600000

0.800000

1.000000

1.200000

1 2 3 4 5 6 7 8 9 10

R2

R2 & MRK

38

Graph 3

Plotting each regression’s R-squares, three sets of regressions’ R-Squares are

plotted; 10 portfolios’ returns against QMJ, 10 portfolios’ against QMJ and Market

factor, and 10 portfolios’ against Fama – French -Three Factor and QMJ

-1.400000

-1.200000

-1.000000

-0.800000

-0.600000

-0.400000

-0.200000

0.000000

0.200000

1 2 3 4 5 6 7 8 9 10QMJ Coefficient

QMJ & MKT Coefficient

QMJ with FFM ThreeFactor

39

Graph 4

Plotting all alphas generated from the six sets of regressions: Mom stands for

Momentum factor, MRK stands for Market Factor, QMJ stands for Quality Minus

Junk Factor, and Fama-French-Three Factor includes, Size Factor, Value Factor,

Market Factor.

-0.060000

-0.040000

-0.020000

0.000000

0.020000

0.040000

0.060000

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

Alp

ha

valu

e

ALPHA Plots

ALPHA

QMJ & MRK

Fama-Three

Fama-Three & QMJ

"Fama-Three & Mom"

Fama-Three & Mom & QMJ

40

7: Reference:

7.1 Mutual Funds’ Researches

Carhart, M. M., (1997). On persistence in mutual fund performance. Journal of Finance 52: 57–82.

Malkiel, B., (1995). Returns from investing in equity mutual Funds 1971 to 1991.Journal of Finance 50:

549-72.

Gruber, M., (1996). Another Puzzle: The growth in actively managed mutual funds. Journal of Finance 52:

783-810.

Souza, A.D., & Lynch A., (2012). Does mutual fund performance vary over the business cycle? Working

Paper.

Pfeiffer, A. S., & Evensky, H. R., (2012). Modern fool’s gold. The Journal of Investing 21: 60-68.

Christopher B. P., Todd S., & Joshua M., (2009). The case for index-fund investing (The Vanguard Group.)

Grinblatt M., & Titman S., (1989). Mutual fund performance: An analysis of quarterly portfolio holdings.

Journal of Business 62: 393-416.

Grinblatt M., & Titman S., (1993). Performance measurement without benchmarks: an examination of

mutual fund returns. Journal of Business 60: 97-112.

Grinblatt M., Titman S., & Wermers. R., (1995). Momentum strategies, portfolio performance and

herding: A study of mutual fund behaviour. American Economic Review 85: 1088-1105

Wermers, R., (1997). Momentum investment strategies of mutual funds, performance persistence, and

survivorship bias. Working paper

Hendricks, D., Patel, J., and Zeckhauser, R., (1993). Hot Hands in Mutual Funds: Short-Run Persistence of

Relative Performance, Journal of Finance 48: 93-130.

Goetzmann, W., & Ibbotson R., (1994). Do Winners Repeat? Patterns in Mutual Fund Performance,

Journal of Portfolio Management 20: 9-18.

Brown S., & Goetzmann W., (1995). Performance persistence, Journal of Finance, 50: 679-698.

41

Elton, E.J., Gruber, M.J., Das S., & Hlavka, M., (1993). Efficiency with Costly Information: A

Reinterpretation of Evidence from Managed Portfolios, Review of Financial Studies 6: 1–22

Elton, E.J., Gruber, M.J., & Blake, C.R., (1996). The Persistence of risk-adjusted Mutual Fund

Performance, Journal of Business 69:133–157.

Elton, E.J., Gruber, M.J., & Blake, C.R., (1996). Survivorship Bias and Mutual Fund Performance, Review

of Financial Studies 9: 1097-1120.

Jegadeesh, N., & Titman, S., (1993). Returns to Buying Winners and Selling Losers: Implications for Stock

Market Efficiency, Journal of finance 4: 65-91

Kacperczyk, M.T., Sialm C. & Lu Zheng L., (2005). On the Industry Concentration of Actively Managed

Equity Mutual Funds, Journal of Finance 6: 1983–2011

Lang, L., & Stulz, R., (1994). Tobin’s Q, corporate diversification, and firm performance. Journal of

Political Economy 102: 1248-1280.

Sapp, Travis, & Xuemin Yan (2008). Security concentration and active fund management: Do focused

funds offer superior performance? The Financial Review 43: 27-49

7.2 Asset Pricing Researches

Markowitz, H. M., (1959). Portfolio Selection: Efficient Diversification of Investments

Sharpe, W. F., (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. Journal

of Finance 19: 425-442.

Treynor, J. L., (1962). Toward a Theory of Market Value of Risky Assets. Unpublished manuscript.

Black, F., Jensen M.C., & Scholes M., (1972). The Capital Asset Pricing Model: Some Empirical Tests

pp: 79–121

Lintner, J., (1965). The Valuation of risk assets and the selection of risky investments in stock portfolios

and capital budgets. The Review of Economics and Statistic 47: 13-37

Mossin, J., (1966). Equilibrium in a Capital Asset Market. Econometrica 34: 768-783

Ross, S. A., (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory 13: 341-

360

Asness, C.S., & Frazzini, A., (2013). The Devil in HML’s Detail Journal of Portfolio Management 39: 49-

68.

42

Fama, E. F., & French, K. R., (1996). Multifactor explanations of asset pricing anomalies. Journal of

Finance 51(1): 55-84.

Fama, E. F., & French, K.R., (1992). The cross-section of expected stock returns. Journal of Finance 47(2):

427-465.

Fama, E. F., & French, K. R., (1993). Common risk factors in the returns on stocks and bonds. Journal of

Financial Economics 33(1): 3-56.

Jensen, M.C., (1969). Risk, the pricing of capital assets, and evaluation of investment portfolios. Journal of

Business 42: 167-247.

Lakonishok, J., Shleifer, A., & Vishny, R,W., (1994). Contrarian Investment Extrapolation and Risk. The

Journal of Finance 49: 1541-1578

Asness, C.S., Moskowitz, T.J. & Pedersen, L.H., (2009). Value and Momentum Everywhere. National

Bureau of Economic Research Working Papers

Hou, K., Xue, C., & Zhang L., (2012). Digesting Anomalies: An Investment Approach. NBER working

paper

Fama, E. F., & French, K. R., (2013). A Five-Factor Asset Pricing Model. Journal of Financial Economics

116: 1-22

Asness, C, S., & Frazzini, A., & Pedersen, L.H., (2013) Quality Minus Junk

43

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